Interlude for Behavioral Economics

The so-called “ra­tio­nal” solu­tions to the Pri­son­ers’ Dilemma and Ul­ti­ma­tum Game are sub­op­ti­mal to say the least. Hu­mans have var­i­ous kludges added by both na­ture or nur­ture to do bet­ter, but they’re not perfect and they’re cer­tainly not sim­ple. They leave en­tirely open the ques­tion of what real peo­ple will ac­tu­ally do in these situ­a­tions, a ques­tion which can only be ad­dressed by hard data.

As in so many other ar­eas, our most im­por­tant in­for­ma­tion comes from re­al­ity tele­vi­sion. The Art of Strat­egy dis­cusses a US game show “Friend or Foe” where a team of two con­tes­tants earned money by an­swer­ing trivia ques­tions. At the end of the show, the team used a sort-of Pri­soner’s Dilemma to split their win­nings: each team mem­ber chose “Friend” (co­op­er­ate) or “Foe” (defect). If one player co­op­er­ated and the other defected, the defec­tor kept 100% of the pot. If both co­op­er­ated, each kept 50%. And if both defected, nei­ther kept any­thing (this is a sig­nifi­cant differ­ence from the stan­dard dilemma, where a player is a lit­tle bet­ter off defect­ing than co­op­er­at­ing if her op­po­nent defects).

Play­ers chose “Friend” about 45% of the time. Sig­nifi­cantly, this num­ber re­mained con­stant de­spite the size of the pot: they were no more likely to co­op­er­ate when split­ting small amounts of money than large.

Play­ers seemed to want to play “Friend” if and only if they ex­pected their op­po­nents to do so. This is not ra­tio­nal, but it ac­cords with the “Tit-for-Tat” strat­egy hy­poth­e­sized to be the evolu­tion­ary solu­tion to Pri­soner’s Dilemma. This played out on the show in a sur­pris­ing way: play­ers’ choices started off ran­dom, but as the show went on and con­tes­tants be­gan par­ti­ci­pat­ing who had seen pre­vi­ous epi­sodes, they be­gan to base their de­ci­sion on ob­serv­able char­ac­ter­is­tics about their op­po­nents. For ex­am­ple, in the first sea­son women co­op­er­ated more of­ten than men, so by the sec­ond sea­son a player was co­op­er­at­ing more of­ten if their op­po­nent was a woman—whether or not that player was a man or woman them­selves.

Among the su­perfi­cial char­ac­ter­is­tics used, the only one to reach statis­ti­cal sig­nifi­cance ac­cord­ing to the study was age: play­ers be­low the me­dian age of 27 played “Foe” more of­ten than those over it (65% vs. 39%, p < .001). Other non­signifi­cant ten­den­cies were for men to defect more than women (53% vs. 46%, p=.34) and for black peo­ple to defect more than white peo­ple (58% vs. 48%, p=.33). Th­ese non­signifi­cant ten­den­cies be­came im­por­tant be­cause the play­ers them­selves at­tributed sig­nifi­cance to them: for ex­am­ple, by the sec­ond sea­son women were play­ing “Foe” 60% of the time against men but only 45% of the time against women (p<.01) pre­sum­ably be­cause women were per­ceived to be more likely to play “Friend” back; also dur­ing the sec­ond sea­son, white peo­ple would play “Foe” 75% against black peo­ple, but only 54% of the time against other white peo­ple.

(This risks self-fulfilling prophe­cies. If I am a black man play­ing a white woman, I ex­pect she will ex­pect me to play “Foe” against her, and she will “re­cip­ro­cate” by play­ing “Foe” her­self. There­fore, I may choose to “re­cip­ro­cate” against her by play­ing “Foe” my­self, even if I wasn’t origi­nally in­tend­ing to do so, and other white women might ob­serve this, thus cre­at­ing a vi­cious cy­cle.)

In any case, these at­tempts at co­or­di­nated play worked, but only im­perfectly. By the sec­ond sea­son, 57% of pairs chose the same op­tion—ei­ther (C, C) or (D, D).

Art of Strat­egy in­cluded an­other great Pri­soner’s Dilemma ex­per­i­ment. In this one, the ex­per­i­menters spoiled the game: they told both play­ers that they would be de­cid­ing si­mul­ta­neously, but in fact, they let Player 1 de­cide first, and then se­cretly ap­proached Player 2 and told her Player 1′s de­ci­sion, let­ting Player 2 con­sider this in­for­ma­tion when mak­ing her own choice.

Why should this be in­ter­est­ing? From the pre­vi­ous data, we know that hu­mans play “tit-for-ex­pected-tat”: they will gen­er­ally co­op­er­ate if they be­lieve their op­po­nent will co­op­er­ate too. We can come up with two hy­pothe­ses to ex­plain this be­hav­ior. First, this could be a folk ver­sion of Time­less De­ci­sion The­ory or Hofs­tadter’s su­per­ra­tional­ity; a be­lief that their own de­ci­sion liter­ally de­ter­mines their op­po­nent’s de­ci­sion. Se­cond, it could be based on a be­lief in fair­ness: if I think my op­po­nent co­op­er­ated, it’s only de­cent that I do the same.

The “re­searchers spoil the setup” ex­per­i­ment can dis­t­in­guish be­tween these two hy­pothe­ses. If peo­ple be­lieve their choice de­ter­mines that of their op­po­nent, then once they know their op­po­nent’s choice they no longer have to worry and can freely defect to max­i­mize their own win­nings. But if peo­ple want to co­op­er­ate to re­ward their op­po­nent, then learn­ing that their op­po­nent co­op­er­ated for sure should only in­crease their will­ing­ness to re­cip­ro­cate.

The re­sults: If you tell the sec­ond player that the first player defected, 3% still co­op­er­ate (ap­par­ently 3% of peo­ple are Je­sus). If you tell the sec­ond player that the first player co­op­er­ated.........only 16% co­op­er­ate. When the same re­searchers in the same lab didn’t tell the sec­ond player any­thing, 37% co­op­er­ated.

This is a pretty re­sound­ing vic­tory for the “folk ver­sion of su­per­ra­tional­ity” hy­poth­e­sis. 21% of peo­ple wouldn’t co­op­er­ate if they heard their op­po­nent defected, wouldn’t co­op­er­ate if they heard their op­po­nent co­op­er­ated, but will co­op­er­ate if they don’t know which of those two their op­po­nent played.

Mov­ing on to the Ul­ti­ma­tum Game: very broadly, the first player usu­ally offers be­tween 30 and 50 per­cent, and the sec­ond player tends to ac­cept. If the first player offers less than about 20 per­cent, the sec­ond player tends to re­ject it.

Like the Pri­soner’s Dilemma, the amount of money at stake doesn’t seem to mat­ter. This is re­ally sur­pris­ing! Imag­ine you played an Ul­ti­ma­tum Game for a billion dol­lars. The first player pro­poses $990 mil­lion for her­self, $10 mil­lion for you. On the one hand, this is a 99-1 split, just as un­fair as $99 ver­sus $1. On the other hand, ten mil­lion dol­lars!

Although ty­coons have yet to donate a billion dol­lars to use for Ul­ti­ma­tum Game ex­per­i­ments, re­searchers have done the next best thing and flown out to Third World coun­tries where even $100 can be an im­pres­sive amount of money. In games in In­done­sia played for a pot con­tain­ing a sixth of In­done­si­ans’ av­er­age yearly in­come, In­done­si­ans still re­jected un­fair offers. In fact, at these lev­els the first player tended to pro­pose fairer deals than at lower stakes—maybe be­cause it would be a dis­aster if her offer get re­jected.

It was origi­nally be­lieved that re­sults in the Ul­ti­ma­tum Game were mostly in­de­pen­dent of cul­ture. Groups in the US, Is­rael, Ja­pan, Eastern Europe, and In­done­sia all got more or less the same re­sults. But this el­e­gant sim­plic­ity was, like so many other things, ru­ined by the Machiguenga In­di­ans of east­ern Peru. They tend to make offers around 25%, and will ac­cept pretty much any­thing.

One more in­ter­est­ing find­ing: peo­ple who ac­cept low offers in the Ul­ti­ma­tum Game have lower testos­terone than those who re­ject them.

There is a cer­tain de­gen­er­ate form of the Ul­ti­ma­tum Game called the Dic­ta­tor Game. In the Dic­ta­tor Game, the sec­ond player doesn’t have the op­tion of ve­to­ing the first player’s dis­tri­bu­tion. In fact, the sec­ond player doesn’t do any­thing at all; the first player dis­tributes the money, both play­ers re­ceive the amount of money the first player de­cided upon, and the game ends. A perfectly self­ish first player would take 100% of the money in the Dic­ta­tor Game, leav­ing the sec­ond player with noth­ing.

In a meta­anal­y­sis of 129 pa­pers con­sist­ing of over 41,000 in­di­vi­d­ual games, the av­er­age amount the first player gave the sec­ond player was 28.35%. 36% of first play­ers take ev­ery­thing, 17% di­vide the pot equally, and 5% give ev­ery­thing to the sec­ond player, nearly dou­bling our pre­vi­ous es­ti­mate of what per­cent of peo­ple are Je­sus.

The meta-anal­y­sis checks many differ­ent re­sults, most of which are in­signifi­cant, but a few stand out. Sub­jects play­ing the dic­ta­tor game “against” a char­ity are much more gen­er­ous; up to a quar­ter give ev­ery­thing. When the ex­per­i­menter promises to “match” each dol­lar given away (eg the dic­ta­tor gets $100, but if she gives it to the sec­ond player the sec­ond player gets $200), the dic­ta­tor gives much more (some­what sur­pris­ing, as this might be an ex­cuse to keep $66 for your­self and get away with it by claiming that both play­ers still got equal money). On the other hand, if the ex­per­i­menters give the sec­ond player a free $100, so that they start off richer than the dic­ta­tor, the dic­ta­tor com­pen­sates by not giv­ing them nearly as much money.

Old peo­ple give more than young peo­ple, and non-stu­dents give more than stu­dents. Peo­ple from “prim­i­tive” so­cieties give more than peo­ple from more de­vel­oped so­cieties, and the more prim­i­tive the so­ciety, the stronger the effect. The most im­por­tant fac­tor, though? As always, sex. Women both give more and get more in dic­ta­tor games.

It is some­what in­spiring that so many peo­ple give so much in this game, but be­fore we be­come too ex­cited about the fun­da­men­tal good­ness of hu­man­ity, Art of Strat­egy men­tions a great ex­per­i­ment by Dana, Cain, and Dawes. The sub­jects were offered a choice: ei­ther play the Dic­ta­tor Game with a sec­ond player for $10, or get $9 and the sec­ond sub­ject is sent home and never even knows what the ex­per­i­ment is about. A third of par­ti­ci­pants took the sec­ond op­tion.

So gen­eros­ity in the Dic­ta­tor Game isn’t always about want­ing to help other peo­ple. It seems to be about know­ing, deep down, that some anony­mous per­son who prob­a­bly doesn’t even know your name and who will never see you again is dis­ap­pointed in you. Re­move the lit­tle prob­lem of the other per­son know­ing what you did, and they will not only keep the money, but even be will­ing to pay the ex­per­i­ment a dol­lar to keep them quiet.